#### Volume 13, issue 1 (2013)

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Proof of a stronger version of the AJ Conjecture for torus knots

### Anh T Tran

Algebraic & Geometric Topology 13 (2013) 609–624
##### Abstract

For a knot $K$ in ${S}^{3}$, the ${sl}_{2}$–colored Jones function ${J}_{K}\left(n\right)$ is a sequence of Laurent polynomials in the variable $t$ that is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of $K$. The AJ Conjecture (see Garoufalidis [Proceedings of the Casson Fest (2004) 291–309]) states that when reducing $t=-1$, the recurrence polynomial is essentially equal to the $A$–polynomial of $K$. In this paper we consider a stronger version of the AJ Conjecture, proposed by Sikora [arxiv:0807.0943], and confirm it for all torus knots.

##### Keywords
colored Jones polynomial, $A$–polynomial, AJ Conjecture
Primary: 57N10
Secondary: 57M25